$12^{2}_{340}$ - Minimal pinning sets
Pinning sets for 12^2_340 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_340 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 256
of which optimal: 1
of which minimal: 1
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.96564
on average over minimal pinning sets: 2.0
on average over optimal pinning sets: 2.0
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 9}
4
[2, 2, 2, 2]
2.00
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
1
0
0
2.0
5
0
0
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,5,5],[0,6,6,3],[0,2,7,7],[0,8,8,1],[1,9,6,1],[2,5,9,2],[3,9,8,3],[4,7,9,4],[5,8,7,6]]
PD code (use to draw this multiloop with SnapPy): [[10,5,1,6],[6,11,7,20],[15,9,16,10],[16,4,17,5],[1,12,2,11],[7,19,8,20],[8,14,9,15],[3,17,4,18],[12,3,13,2],[13,18,14,19]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (10,11,-1,-12)(15,2,-16,-3)(8,3,-9,-4)(14,7,-15,-8)(6,13,-7,-14)(1,16,-2,-17)(12,17,-13,-18)(5,18,-6,-19)(19,4,-20,-5)(20,9,-11,-10)
Edge permutation $\epsilon=$ (-1,1)(-2,2)(-3,3)(-4,4)(-5,5)(-6,6)(-7,7)(-8,8)(-9,9)(-10,10)(-11,11)(-12,12)(-13,13)(-14,14)(-15,15)(-16,16)(-17,17)(-18,18)(-19,19)(-20,20)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-17,12)(-2,15,7,13,17)(-3,8,-15)(-4,19,-6,-14,-8)(-5,-19)(-7,14)(-9,20,4)(-10,-12,-18,5,-20)(-11,10)(-13,6,18)(-16,1,11,9,3)(2,16)
Multiloop annotated with half-edges
12^2_340 annotated with half-edges